PHY PHY 1214 1214 General General Physics Physics II II

Lecture 26 Refraction and Dispersion July 18, 2005

Transparent Optical Media

Rather surprisingly, there are types of matter, solids, liquids, and gasses, that are transparent and that transmit light almost unimpeded. When you consider that such matter is made of atoms, electrically charged nuclei orbited by clouds of electrically charged electrons, it is quite remarkable that electromagnetic radiation, the carrier of electric fields that interact strongly with these charged particles, is not immediately absorbed. Instead, within the transparent medium the bound electrons vibrate together at the frequency of the incoming electric field to help along the incident light without absorbing its energy, but usually reducing its speed through the material as it is transmitted.July 18, 2005 PHY 1214 - Lecture 25 3

RefractionWhen light is incident on a smooth boundary between two transparent materials (e.g., air and glass), two things happen: 1. Part of the light reflects from the boundary, obeying the law of reflection. 2. Part of the light crosses the boundary, changes direction, and continues into the second medium. This is called refraction.

PHY 1214 - Lecture 25

Willebrord van Roijen Snell 1580 - 1626

The Dutch physicist and mathematician Willebrord Snell of the University of Leiden, in 1621 discovered the law of refraction, also called Snells Law.5

The Index of Refraction

Light travels through transparent media at a speed less than its speed c in vacuum. We define the index of refraction in a transparent medium as:

c vmedium

Is n1 always? Mostly. There are media in which the phase velocity of light waves is greater than c, but this cannot be used to send signals or energy at a speed greater than c.

July 18, 2005

PHY 1214 - Lecture 25

Snells Law and Huygens Principle

We can derive Snells Law from Huygens Principle. Consider a wave front crossing the boundary between media, with the light wavelets traveling at speed v1 in medium 1 and at v2 in medium 2. Constructing the Huygens wavelets at points A, B, and C allows us to fund the position of the new wave front, which has a slightly different direction in the second medium.

Total Internal Reflection

Suppose instead we have a 450-450-900 prism with n=1.50. At what angle will a beam normal to the long side be deflected?

1 = 45

2 = sin 1 (1.5sin 1 ) = sin 1 (1.061)

There is no such angle! Therefore, there

will be no refracted ray, and the light will be completely reflected. This is called total internal reflection. It occurs only when the 2nd medium has a lower index of refraction than the 1st medium (n2<n1), and when c.

n c = sin 2 n1 1

When 1=c, 2=900.

July 18, 2005

PHY 1214 - Lecture 25

10

Example: Total Internal Reflection

A light bulb is set in the bottom of a 3.0 m deep swimming pool. What is the diameter of the ring of light seen on the pools surface?

c = sin 1

1.0 = 48.7 1.33

D = 2h tan c = 2(3.0 m) tan(48.7) = 6.83 m

This is the so-called ring of bright water seen when looking up from within a pool of water. The outside world is compressed to lie within the ring.

(a) (b) (c) (d)

July 18, 2005

PHY 1214 - Lecture 25

13

Image Formation by Refraction

l = s tan 1 = s ' tan 2

s' = s' tan 1 s tan 2 n2 s n1PHY 1214 - Lecture 25 14

n2 sin 1 tan 1 = n1 sin 2 tan 2

July 18, 2005

Example: Air Bubble in a Window

A fish and a sailor look at each other through the 5.0 cm thick glass port hole of a submarine. There is a small air bubble half way through the glass. How far behind the glass surface does the bubble appear to the fish? How far behind the glass surface does the bubble appear to the sailor?n = 1.50 Glass n = 1.00 Air n = 1.33 Water

s '(fish)

n2 (1.33) s= (2.5 cm) = 2.2 cm n1 (1.50)

n2 (1.00) s= (2.5 cm) = 1.7 cm n1 (1.50)

s '(sailor)

July 18, 2005

PHY 1214 - Lecture 25

15

Experiments with light and prisms show the following:

Color and Dispersion

1. What we perceive as white light is actually a mixture of all colors. White light can be disbursed into colors and, equally important, colors can be combined to produce white light. 2. The index of refraction is slightly different for different colors of light. Glass has a slightly higher index of refraction for violet light than for green or red light. Consequently, different colors refract at slightly different angles.

July 18, 2005

PHY 1214 - Lecture 25

16

DispersionThis can be made quantitative by measuring the index of refraction of a transparent material as a function of wavelength and associating wavelengths with colors..

July 18, 2005

PHY 1214 - Lecture 25

17

Example: Dispersing Light with a Prism

We saw that light incident on a 300 prism is deflected by 22.60 if the prisms index of refraction is 1.59. Suppose this is the index of refraction for deep violet light, and that deep red light has an index of refraction of 1.54. (a) What is the deflection angle for deep red light? (b) If a beam of white light is dispersed by the prism, how wide is the rainbow spectrum on a screen 2.0 m away>n1 = 1.54; violet = 52.6; violet = 22.6